The Portuguese, who left Real Madrid last weekend, won the 2005 and 2006 Premier League titles in his first spell with the west London club but departed in 2007 after falling out with billionaire owner Roman Abramovich.
"I am delighted to welcome Jose back to Chelsea. His continued success, drive and ambition made him the outstanding candidate," said chief executive Ron Gourlay in a club statement.
"It is our aim to keep the club moving forward to achieve greater success in the future and Jose is our number one choice as we believe he is the right manager to do just that.
"He was and remains a hugely popular figure at the club and everyone here looks forward to working with him again."
Mourinho grinned broadly as he spoke of his delight at returning to Stamford Bridge.
"Now I can say I am one of you," he told Chelsea TV as he gave a message to the fans. "I never hide that in football I have two great passions - Inter Milan and Chelsea - and Chelsea is more than important for me.
"It was very, very hard to play against Chelsea and I did it only twice," he said referring to the time he led Inter to victory in a 2010 Champions League first knockout round tie.
"Now I promise the same things I promised in 2004 with this difference to add - that I am one of you."
The news of his return was an open secret long before Mourinho told a Spanish TV football show on Sunday that he hoped to take charge at Chelsea by the end of the week.
"I feel the people there love me and in life you have to look for that," said the 50-year-old, who first joined Chelsea in 2004 and ended their 50-year wait for a top flight title as well as winning the FA Cup in 2007 and the League Cup twice.
"Life is beautiful and short and you must look for what you think is best for you," added Mourinho, who has also enjoyed successful spells as coach of Porto and Inter, winning the Champions League with both.
Mourinho ended his three-year reign at Real Madrid with a 4-2 home La Liga victory over Osasuna at the weekend. He won the Spanish title in 2012 but left after a difficult season with no major trophies.
FANS HAPPY
Mourinho will be accompanied by three staff - Rui Faria, Silvino Louro and Jose Morais - as assistant first team coaches working alongside current first team staff Steve Holland, Christophe Lollichon and Chris Jones.
Chelsea said he will be officially presented at a news conference at Stamford Bridge on Monday, June 10.
The news was welcomed by Chelsea fans, pining for his return ever since 2007 despite the club's success in winning the Champions League under Italian Roberto Di Matteo in 2012.
The November appointment of unpopular former Liverpool manager Rafael Benitez as interim coach, in place of the sacked Di Matteo, only increased the clamour for Mourinho.
"I think 95 percent of the Chelsea supporters are pleased that Jose's come back," the club's former defender Ron 'Chopper' Harris told Sky Sports television. "I think it's a pat on the back fo
